Problem: Solve the equation. $\dfrac{5}7 =p+\dfrac47$ $p=$
Solution: Let's subtract to get $p$ by itself. $\begin{aligned}\dfrac{5}7 &=p+\dfrac47 \\ \\ \dfrac57 {-\dfrac47}&= p+\dfrac47{-\dfrac47}~~~~~~~~{\text{subtract }\dfrac47} \text{ from each side to get } p \text{ by itself }\\ \\ \dfrac57 {-\dfrac47}&= p+\cancel{\dfrac47}{-}\cancel{{\dfrac47}} \\ \dfrac57 {-\dfrac47} &= p\end{aligned}$ The answer: $p={\dfrac17}$ Let's check to make sure. $\begin{aligned} \dfrac{5}7 &=p+\dfrac47\\\\ \dfrac57&\stackrel{?}{=} {\dfrac17}+\dfrac47 \\\\ \dfrac57 &= \dfrac57 ~~~~~~~~~~~~~~~~~~\text{Yes!} \end{aligned}$